Question

Trading Momenta in a Collision

Two particles
moveperpendicular to each other until they collide. Particle 1 has mass and momentum of magnitude , and particle 2 has mass and momentum of magnitude .Note: Magnitudes are not drawn to scale in any of
thefigures.

Part A

Suppose that after the collision,
theparticles "trade" their momenta, as shown in the figure. That
is,particle 1 now has magnitude of momentum , and particle 2 has magnitude of momentum ; furthermore, each particle is now moving in
thedirection in which the other had been moving. How much
kineticenergy, , is lost in the collision?

Express your answer in terms
ofand .

=

Correct

Part B

Consider an alternative situation: This
timethe particles collide completely inelastically. How much
kineticenergy is lost in this case?